Related Rates: A plane, 40 mi from airport, is flying at

Limits, differentiation, related rates, integration, trig integrals, etc.
bbsa3412
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Related Rates: A plane, 40 mi from airport, is flying at

Postby bbsa3412 » Wed Mar 17, 2010 8:16 am

Need some help setting up the following problem:

A plane is 40 miles (horizontally away from an airport) flying at a constant altitude of 4 miles. The radar at the airport determines that the distance from the plane to the radar dish is changing at 240 mph. Determine the speed of the plane.

nona.m.nona
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Re: Related Rates: A plane, 40 mi from airport, is flying at

Postby nona.m.nona » Wed Mar 17, 2010 11:59 am

Start with the triangle: the height line at the airport, labelled with "y = 4"; the horizontal line for the flight path, labelled with "x = 40"; and the hypotenuse, labelled with dD/dt = 240. You are given that dy/dt = 0, and the Pythagorean Theorem gives you that x2 + y2 = D2.

Differentiate implicitly with respect to time, and then plug in the known values. Solve for dx/dt.

bbsa3412
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Re: Related Rates: A plane, 40 mi from airport, is flying at

Postby bbsa3412 » Wed Mar 17, 2010 11:00 pm

Thank you, this helped greatly.


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